I know that a video interlace mode was available on the Apple /// prototype and eventually on the Apple ///+, but I haven't seen anything that says what it was for. Did it provide a higher resolution mode or was it simply to fill in the horizontal raster gaps?
According to the Apple III Plus Owner's Guide, the interlace mode is called "text interlace":
text interlace a Feature of the Apple III console that, when activated, increases the resolution of text characters on the display screen.
Page 39 provides a little more detail:
So "text interlace" is simply a mode designed to enhance the appearance of text characters on the screen, without using any additional video memory, or even character ROM! It achieves this by switching from a progressive (non-interlaced) resolution of 560×192 pixels to an interlaced resolution of 560×384 pixels and doubling each row of pixels to stretch each 7×8 character into a 7×16 matrix. But note:
Text interlace works best with green-phosphor and other long-persistence video displays. If you have a black-and-white or color display, text interlace may make the picture flicker.